The difference between LGA 1156 and 1366 is 210 pins, and the ability to host different CPU's where the LGA 1156 is geared to more mainstream audiences and the 1366 is designed for more of an enthusiast or powerhouse audience. However the chipsets on the motherboards that go onto these things are a whole different story.
The LGA 1156 has a total of 4 available chipsets to choose from. They are the P55, H55, H57 and the Q67. All four have a DMI Bus Interface which are rated at 2 GB/s and that's where the similarities stop.
The H55 is the low end with only 6 PCI-E channels, to put it in perspective, modern graphics cards use 16 of them, but are nearly fully powered and functional with 8. It does come with an IGP, but can only be host to 12 USB devices.
The P55 is the mid range with 8 PCI-E Lanes, and 14 USB slots, but it doesn't come with an IGP.
The other two, H57 and Q57 are pretty much in a tie with the main difference being TDP, and intel proprietardy features like "Intel® Quiet System Technology" nothing really major. These guys have 8 PCI-E lanes, and can be host to 14 USB devices.
Then of course we have the chipset for the LGA 1366 which comes in one flavor for desktop pc usage and that is the X58. This one has no IGP, but comes with 36 PCI-E lanes, yes 36, i'm not sure about the USB capabilities, but I'm more than sure that it's greater than or equal to the best 1156 chipset.
To go a little further though, these are now considered outdated sockets as intel has just released (and recalled) the LGA 1155 chipset for their low end and mid range CPU's, and is soon to release the LGA 2011 chipset for the High end and Enthusiast CPU's.
Whoops, forgot to add.
The 1156's are limited to dual channel memory, and 4 slots of it which allows a max of 16GB of memory, the 1366's are limited to triple-channel memory and 6 slots of it which allows 24GB of memory. I believe the LGA 1155 is similar to the 1156, dual channel with 4 spaces, and the 2011 with QUAD channel and 8 spaces...although I can't verify that.